Existence of periodic solutions for a 2nth-order nonlinear difference equation ✩

The authors consider the 2nth-order difference equation n rt−n nxt−n +f (t,xt ) = 0, n∈ Z(3), t ∈ Z, where f :Z × R→R is a continuous function in the second variable, f (t + T,z) = f (t,z) for all (t, z) ∈ Z × R, rt+T = rt for all t ∈ Z, and T a given positive integer. By the Linking Theorem, some new criteria are obtained for the existence and multiplicity of periodic solutions of the above equation. © 2006 Elsevier Inc. All rights reserved.